Problem: Simplify the following expression: $ x = \dfrac{5z}{8z + 9} + \dfrac{4}{3} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{3}{3}$ $ \dfrac{5z}{8z + 9} \times \dfrac{3}{3} = \dfrac{15z}{24z + 27} $ Multiply the second expression by $\dfrac{8z + 9}{8z + 9}$ $ \dfrac{4}{3} \times \dfrac{8z + 9}{8z + 9} = \dfrac{32z + 36}{24z + 27} $ Therefore $ x = \dfrac{15z}{24z + 27} + \dfrac{32z + 36}{24z + 27} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{15z + 32z + 36}{24z + 27} $ $x = \dfrac{47z + 36}{24z + 27}$